MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES

doi:10.1016/S0252-9602(16)30127-8

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 223-234.doi: 10.1016/S0252-9602(16)30127-8

MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES

杨青^1,2, 朱家砚^3,4, 李正帮⁵

1. School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China;
3. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
4. School of Information and Communication, Wuhan College, Wuhan 430079, China;
5. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China

收稿日期:2015-09-07 修回日期:2016-04-29 出版日期:2017-02-25 发布日期:2017-02-25
通讯作者: Zhengbang LI,E-mail:lizhengbang@mail.ccnu.edu.cn E-mail:lizhengbang@mail.ccnu.edu.cn
作者简介:Qing YANG,E-mail:13554546673@163.com;Jiayan ZHU,E-mail:zhujy999@outlook.com
基金资助:
This work is partially supported by the Natural Science Foundation of China (11401240, 11471135), and the self-determined research funds of CCNU from the colleges' basic research of MOE (CCNU15A05038, CCNU15ZD011).

MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES

Qing YANG^1,2, Jiayan ZHU^3,4, Zhengbang LI⁵

1. School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China;
3. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
4. School of Information and Communication, Wuhan College, Wuhan 430079, China;
5. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China

Received:2015-09-07 Revised:2016-04-29 Online:2017-02-25 Published:2017-02-25
Contact: Zhengbang LI,E-mail:lizhengbang@mail.ccnu.edu.cn E-mail:lizhengbang@mail.ccnu.edu.cn
About author:Qing YANG,E-mail:13554546673@163.com;Jiayan ZHU,E-mail:zhujy999@outlook.com
Supported by:
This work is partially supported by the Natural Science Foundation of China (11401240, 11471135), and the self-determined research funds of CCNU from the colleges' basic research of MOE (CCNU15A05038, CCNU15ZD011).

摘要/Abstract

摘要：

We propose the maximin efficiency robust test (MERT) for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test. We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more. We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied. Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.

关键词: maximin efficiency robust, multiple nuisance parameters, score test, statistical power

Abstract:

Key words: maximin efficiency robust, multiple nuisance parameters, score test, statistical power

杨青, 朱家砚, 李正帮. MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES[J]. 数学物理学报(英文版), 2017, 37(1): 223-234.

Qing YANG, Jiayan ZHU, Zhengbang LI. MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES[J]. Acta mathematica scientia,Series B, 2017, 37(1): 223-234.

参考文献

[1] Serfling R J. Approximation Theorems of Mathematical Statistics. New York:John Wiley & Sons, 1980
[2] Noether G E. On a theorem of Pitman. Ann Math Statist, 1955, 26:64-68
[3] Gastwirth J L. On robust procedures. J Amer Stat Ass, 1966, 61:929-948
[4] Gastwirth J L. The use of maximin efficiency robust tests in combining contingency tables and survival analysis. J Amer Stat Ass, 1985, 80:380-384
[5] Zheng G, Li Q Z, Yuan A. Some statistical properties of efficiency robust test with applications to genetic association studies. Scand J Stat Theory Appl, 2014, 41:762-774
[6] Birnbaum A, Laska E. Efficiency robust 2-sample rank test. J Amer Stat Ass, 1967, 62:1241-1251
[7] Barndorff-Nielsen O E, Cox D R. Inference and Asymptotics. Florida:Chapman and Hall/CRC Press, 1994
[8] Gastwirth J L, Freidlin B. On power and efficiency robust linkage tests for affected sibs. Ann Hum Genet, 2000, 64:443-453
[9] Freidlin B, Zheng G, Li Z, Gastwirth J L. Trend tests for case-ontrol studies of genetic markers:power, sample size and robustness. Hum Hered, 2002, 53:146-152
[10] So H-C, Sham P C. Robust association tests under differrent genetic models, allowing for binary or quantitative trait and covariate. Behav Genet, 2011, 41:768-775
[11] Schaid D J, Sommer S S. Genotype relative risks-methods for design and analysis of candidate-gene association studies. Am J Hum Genet, 1993, 53:1114-1126
[12] Sasieni P D. From genotypes to genes:doubling the sample size. Biometrics, 1997, 53:1253-1261
[13] CochranWG. Some methods for strengthening the common chi-square tests. Biometrics, 1954, 10:417-451
[14] Armitage P. Tests for linear trends in proportions and frequencies. Biometrics, 1955, 11:375-386
[15] Zheng G, Joo J, Yang Y. Pearson's test, trend test and MAX are all trends tests with different types of scores. Ann Hum Genet, 2009, 73:133-140
[16] Xiong M, Zhao J, Boerwinkle E. Generalized T² test for genome association studies. Am J Hum Genet, 2002, 70:1257-1268
[17] Chapman J M, Cooper J D, Todd J A, Clayton D G. Detecting disease associations due to linkage disequi-ibrium using haplotype tags:a class of tests and the determinants of statistical power. Hum Hered, 2003, 56:18-31
[18] Fan R, Knapp M. Genome association studies of complex diseases by case-control designs. Am J Hum Genet, 2003, 72:850-868
[19] Li Q Z, Zheng G, Li Z H, Yu K. Efficient Approximation of P-value of the Maximum of Correlated Tests, with Applications to Genome-Wide Association Studies. Ann Human Genetics, 2008, 72:397-406
[20] Chatterjee N, Chen Y-H, Luo S, Carroll R J. Analysis of Case-Control Association Studies:SNPs, Imputation and Haplotypes. Stat Sci, 2009, 24:489-502
[21] Ballard D H, Cho J, Zhao, H Y. Comparisons of multi-marker association methods to detect association between a candidate region and disease. Genetic Epidemiology, 2010, 34:201-212

MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES

MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES

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